Book Image

Scientific Computing with Scala

By : Vytautas Jancauskas
Book Image

Scientific Computing with Scala

By: Vytautas Jancauskas

Overview of this book

Scala is a statically typed, Java Virtual Machine (JVM)-based language with strong support for functional programming. There exist libraries for Scala that cover a range of common scientific computing tasks – from linear algebra and numerical algorithms to convenient and safe parallelization to powerful plotting facilities. Learning to use these to perform common scientific tasks will allow you to write programs that are both fast and easy to write and maintain. We will start by discussing the advantages of using Scala over other scientific computing platforms. You will discover Scala packages that provide the functionality you have come to expect when writing scientific software. We will explore using Scala's Breeze library for linear algebra, optimization, and signal processing. We will then proceed to the Saddle library for data analysis. If you have experience in R or with Python's popular pandas library you will learn how to translate those skills to Saddle. If you are new to data analysis, you will learn basic concepts of Saddle as well. Well will explore the numerical computing environment called ScalaLab. It comes bundled with a lot of scientific software readily available. We will use it for interactive computing, data analysis, and visualization. In the following chapters, we will explore using Scala's powerful parallel collections for safe and convenient parallel programming. Topics such as the Akka concurrency framework will be covered. Finally, you will learn about multivariate data visualization and how to produce professional-looking plots in Scala easily. After reading the book, you should have more than enough information on how to start using Scala as your scientific computing platform
Table of Contents (16 chapters)
Scientific Computing with Scala
About the Author
About the Reviewer

Improving the program

There is a slight improvement that we will leave as an exercise to the reader. If you run the program as it is presented here, you will note that it runs rather slowly. The reason for this is that we approximate the gradient. This is computationally costly since it involves multiple evaluations of the Sammon error function. We could do better than this. We can implement the gradient calculation ourselves. The formula to calculate the gradient is given in the equation here.

The notation in the equation is the same as earlier. The equation will calculate the value of the gradient at the kth coordinate of the ith vector of the approximation. Keep in mind that, since the stress function in our case is 300-dimensional, it means that to approximate the derivative you will need to evaluate the function at least 600 times (if the simplest method for approximating derivatives is used); that is, if you choose to approximate the derivative. We can implement the calculation of the...